I need to know how to find the polar coordinates of (21, 48); I figured out r (52.4) but I can't figure out the theta even after so many instructional videos! I have the answer (Theta is 66.4) but I can't figure out how to get to it!

Guest May 10, 2017

#2**+4 **

I may not be able to explain any better...but I will try!

Here is just a graph of the point (21, 48).

Theta is the angle that a line from the origin to the point makes with the positive x-axis.

The second one is the same graph, just with some more markings on it.

Look at the second picture. This is just a right triangle! And...in every right triangle,

tan = opposide / adjacent

So..

tan θ = 48/21

θ = atan(48/21)

θ ≈ 66.371º

And we can use the Pythagorean theorem to find the hypotenuse...which is r.

21^{2} + 48^{2} = r^{2}

r = \(\sqrt{441+2304}\approx52.393\) ...just as you found!

hectictar May 10, 2017